Introduction to Algebraic Number Theory

2026/2027

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

Faculty of Mathematics

Course type:

Optional course (faculty)

When:

3, 4 module

Instructor

Zhgoon, Vladimir

Course Syllabus

Abstract

Algebraic number theory is a classical field of mathematics that was formed during the study of solutions to Diophantine equations, as well as through attempts to prove Fermat's theorem. Now it is a vast classical field underlying Arithmetic geometry. In this course, we will recall the basics of Galois theory, consider the so-called branching theory, prove the main theorems on the structure of ideals (decompositions into simple ideals), prove Dirichlet's theorem on the structure of S-units and the finiteness theorem of a class group. We will highlight a very important analogy between the theory of algebraic numbers and the theory of algebraic curves over finite fields.